Maxwell relations

From Thermal-FluidsPedia

The fundamental thermodynamic relation for a reversible process in a single-component system, where the only work term considered is pdV, is obtained from eq. from Thermodynamic property relations, i.e.,

and dz is an exact differential, as thermodynamic properties like E,H,F, and G are path-independent functions.

Since eq. (5) is the total differential of function z,M and N are related by

Applying eq. (8) to eqs. (1) – (4), the following relationships are obtained:

which are referred to as Maxwell relations. The goal of Maxwell relations is to find equivalent partial derivatives containing p,T, and V that can be physically measured and therefore provide a means of determining the change of entropy, which cannot be measured directly.